mapnoterritory

Bill "Numerical Recipes" Press and Freeman "Dyson sphere" Dyson have a new paper on iterated prisoner dilemas (IPD). Interestingly they found new surprising results: > It is generally assumed that there exists no simple ultimatum strategy whereby one player can enforce a unilateral claim to an unfair share of rewards. Here, we show that such strategies unexpectedly do exist. In particular, a player X who is witting of these strategies can (i) deterministically set her opponent Y’s score, independently of his strategy or response, or (ii) enforce an extortionate linear relation between her and his scores. They discuss a special class of strategies - zero determinant (ZD) strategies of which tit-for-tat (TFT) is a special case: > The extortionate ZD strategies have the peculiar property of sharply distinguishing between “sentient” players, who have a theory of mind about their opponents, and “evolutionary” players, who may be arbitrarily good at exploring a fitness landscape (either locally or globally), but who have no theory of mind. The evolutionary player adjusts his strategy to maximize score, but doesn't take his opponent explicitly into account in another way (hence has "no theory of mind" of the opponent). Possible outcomes are: A) > If X alone is witting of ZD strategies, then IPD reduces to one of two cases, depending on whether Y has a theory of mind. If Y has a theory of mind, then IPD is simply an ultimatum game (15, 16), where X proposes an unfair division and Y can either accept or reject the proposal. If he does not (or if, equivalently, X has fixed her strategy and then gone to lunch), then the game is dilemma-free for Y. He can maximize his own score only by giving X even more; there is no benefit to him in defecting. B) > If X and Y are both witting of ZD, then they may choose to negotiate to each set the other’s score to the maximum cooperative value. Unlike naive PD, there is no advantage in defection, because neither can affect his or her ow